We develop statistical methods for tackling two important problems in genetic association studies. First, we propose a Bayesian approach to overcome the winner's curse in genetic studies. Second, we consider a Bayesian latent variable model for analyzing longitudinal family data with pleiotropic phenotypes. Winner's curse in genetic association studies refers to the estimation bias of the reported odds ratios (OR) for an associated genetic variant from the initial discovery samples. It is a consequence of the sequential procedure in which the estimated effect of an associated genetic marker must first pass a stringent significance threshold. We propose a hierarchical Bayes method in which a spike-and-slab prior is used to account for the possibility that the significant test result may be due to chance. We examine the robustness of the method using different priors corresponding to different degrees of confidence in the testing results and propose a Bayesian model averaging procedure to combine estimates produced by different models. The Bayesian estimators yield smaller variance compared to the conditional likelihood estimator and outperform the latter in the low power studies. We investigate the performance of the method with simulations and applications to four real data examples. Pleiotropy occurs when a single genetic factor influences multiple quantitative or qualitative phenotypes, and it is present in many genetic studies of complex human traits. The longitudinal family studies combine the features of longitudinal studies in individuals and cross-sectional studies in families. Therefore, they provide more information about the genetic and environmental factors associated with the trait of interest. We propose a Bayesian latent variable modeling approach to model multiple phenotypes simultaneously in order to detect the pleiotropic effect and allow for longitudinal and/or family data. An efficient MCMC algorithm is developed to obtain the posterior samples by using hierarchical centering and parameter expansion techniques. We apply spike and slab prior methods to test whether the phenotypes are significantly associated with the latent disease status. We compute Bayes factors using path sampling and discuss their application in testing the significance of factor loadings and the indirect fixed effects. We examine the performance of our methods via extensive simulations and apply them to the blood pressure data from a genetic study of type 1 diabetes (T1D) complications.

We develop statistical methods for tackling two important problems in genetic association studies. First, we propose a Bayesian approach to overcome the winner's curse in genetic studies. Second, we consider a Bayesian latent variable model for analyzing longitudinal family data with pleiotropic phenotypes. Winner's curse in genetic association studies refers to the estimation bias of the reported odds ratios (OR) for an associated genetic variant from the initial discovery samples. It is a consequence of the sequential procedure in which the estimated effect of an associated genetic marker must first pass a stringent significance threshold. We propose a hierarchical Bayes method in which a spike-and-slab prior is used to account for the possibility that the significant test result may be due to chance. We examine the robustness of the method using different priors corresponding to different degrees of confidence in the testing results and propose a Bayesian model averaging procedure to combine estimates produced by different models. The Bayesian estimators yield smaller variance compared to the conditional likelihood estimator and outperform the latter in the low power studies. We investigate the performance of the method with simulations and applications to four real data examples. Pleiotropy occurs when a single genetic factor influences multiple quantitative or qualitative phenotypes, and it is present in many genetic studies of complex human traits. The longitudinal family studies combine the features of longitudinal studies in individuals and cross-sectional studies in families. Therefore, they provide more information about the genetic and environmental factors associated with the trait of interest. We propose a Bayesian latent variable modeling approach to model multiple phenotypes simultaneously in order to detect the pleiotropic effect and allow for longitudinal and/or family data. An efficient MCMC algorithm is developed to obtain the posterior samples by using hierarchical centering and parameter expansion techniques. We apply spike and slab prior methods to test whether the phenotypes are significantly associated with the latent disease status. We compute Bayes factors using path sampling and discuss their application in testing the significance of factor loadings and the indirect fixed effects. We examine the performance of our methods via extensive simulations and apply them to the blood pressure data from a genetic study of type 1 diabetes (T1D) complications.